Boris Tsirelson

Quantum analogues of the Bell inequalities. The case of two spatially separated domains

One Investigates inequalities for the probabilities and mathematical expectations which follow from the postulates of the local quantum theory. It turns out that the relation between the quantum and the classical correlation matrices is expressed] in terms of Grothendiecks known constant. It is also shown that the extremal quantum correlations characterize the Clifford algebra (i.e., canonical anticommutative relations).

Random complex zeroes, I. Asymptotic normality

We consider three models (elliptic, flat and hyperbolic) of Gaussian random analytic functions distinguished by invariance of their zeroes distribution. Asymptotic normality is proven for smooth functionals (linear statistics) of the set of zeroes.

Random complex zeroes, III. Decay of the hole probability

AbstractThe ‘hoe probability’ that a random entire function

The automorphism group of the Gaussian measure cannot act pointwise

\psi (z) = \sum\limits_{k = 0}^\infty {\zeta _k \frac{{z^k }}{{\sqrt {k!} }}} ,

Spectral densities describing off-white noises

where ζ0, ζ1, ... are Gaussian i.i.d. random variables, has no zeroes in the disc of radiusr decays as exp(−cr4) for larger.

Correlated Signals Against Monotone Equilibria

Contrary to the classical wisdom, processes with independent values (defined properly) are much more diverse than white noises combined with Poisson point processes, and product systems are much more diverse than Fock spaces. This text is a survey of recent progress in constructing and investigating nonclassical stochastic flows and continuous products of probability spaces and Hilbert spaces.

Noise as a Boolean algebra of

Classical ergodic theory deals with measure (or measure class) preserving actions of locally compact groups on Lebesgue spaces. An important tool in this setting is a theorem of Mackey which provides spatial models for BooleanG-actions. We show that in full generality this theorem does not hold for actions of Polish groups. In particular there is no Borel model for the Polish automorphism group of a Gaussian measure. In fact, we show that this group as well as many other Polish groups do not admit any nontrivial Borel measure preserving actions.

\sigma

AbstractWe show that the flat chaotic analytic zero points (i.e. zeroes of a random entire function